Extracorporeal membrane oxygenation (ECMO) has been established as a life-saving technique for patients with the most severe forms of respiratory or cardiac failure. It can, however, be associated with severe complications. Anticoagulation therapy is required to prevent ECMO circuit thrombosis. It is, however, associated with an increased risk of hemocoagulation disorders. Thus, safe anticoagulation is a cornerstone of ECMO therapy. The most frequently used anticoagulant is unfractionated heparin, which can, however, cause significant adverse effects. Novel drugs (e.g., argatroban and bivalirudin) may be superior to heparin in the better predictability of their effects, functioning independently of antithrombin, inhibiting thrombin bound to fibrin, and eliminating heparin-induced thrombocytopenia. It is also necessary to keep in mind that hemocoagulation tests are not specific, and their results, used for setting up the dosage, can be biased by many factors. The knowledge of the advantages and disadvantages of particular drugs, limitations of particular tests, and individualization are cornerstones of prevention against critical events, such as life-threatening bleeding or acute oxygenator failure followed by life-threatening hypoxemia and hemodynamic deterioration. This paper describes the effects of anticoagulant drugs used in ECMO and their monitoring, highlighting specific conditions and factors that might influence coagulation and anticoagulation measurements.